hairyberry

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 #1
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Please only ask one question per post.

Number 1: Only A can be expressed in the form ka*x, the others cannot therefore only A is an exponential function.

 

Number 2: 

A) 3^(2y) = 3^5, so 2y =5 y= 5/2

B) 9^(3u+5) = 3^8, 3^(6u+10) = 3^8, 6u + 10 = 8, u = -1/3

C) 8^(4x-1) = 8^10x, 4x -1 = 10x, x= -1/6

 

Number 3:

A) Reflecting a point over the x axis on a graph, (x,y) becomes (x, -y). We can use this to find that reflecting a function over the x axis we get that f(x) becomes -f(x). So after reflecting a exponential function over the x axis y = ka^x becomes y=-ka^x which is an exponential function.

B) Reflecting over the y axis, a point on a graph, (x,y) becomes, (-x,y). We can use this to fine the rule that to reflect a function over the y axis we apply the rule f(x) becomes f(-x). So an exponential function, y=ka^x becomes y=ka^(-x), which is k(1/a)^x, which is also an exponential function.

C)  Like the solutions above, we first translate a point vertically so (x,y) becomes (x,y+h). Applying that to functions in general we see that y or f(x) moves up h, and x stays the same, so a function transformation up h would result in f(x) becoming f(x)+h. Applying this to exponetial functions, a tranlation up h would be y=ka^x + h which is an exponential function. 

D) If a point is translated horizontally by g, then (x,y) would become (x+g, y) . Applying this to this situation, f(x) = ka^x, then moving right by g units would be k(a-g)^x (remember its minus g, minus moves right, plus moves left), which, by out definition is also an exponential function.

Feb 12, 2023